Procedure for the Selection and Validation of a Calibration Model II—Theoretical Basis

Abstract

In the first part of this paper (I-Description and application), an automated, stepwise and analyst-independent process for the selection and validation of calibration models was put forward and applied to two model analytes. This second part presents the mathematical reasoning and experimental work underlying the selection of the different components of this procedure. Different replicate analysis designs (intra/inter-day and intra/inter-extraction) were tested and their impact on test results was evaluated. For most methods, the use of intra-day/intra-extraction measurement replicates is recommended due to its decreased variability. This process should be repeated three times during the validation process in order to assess the time stability of the underlying model. Strategies for identification of heteroscedasticity and their potential weaknesses were examined and a unilateral F-test using the lower limit of quantification and upper limit of quantification replicates was chosen. Three different options for model selection were examined and tested: ANOVA lack-of-fit (LOF), partial F-test and significance of the second-order term. Examination of mathematical assumptions for each test and LC-MS-MS experimental results lead to selection of the partial F-test as being the most suitable. The advantages and drawbacks of ANOVA-LOF, examination of the standardized residuals graph and residuals normality testing (Kolmogorov-Smirnov or Cramer-Von Mises) for validation of the calibration model were examined with the last option proving the best in light of its robustness and accuracy. Choosing the correct calibration model improves QC accuracy, and simulations have shown that this automated scheme has a much better performance than a more traditional method of fitting with increasingly complex models until QC accuracies pass below a threshold.

Systematic optimisation of ethyl glucuronide extraction conditions from scalp hair by design of experiments and its potential effect on cut‐off values appraisal

“…33,34 Determination coefficient (R 2 ), relative standard deviation of the slope, normality of the standardised residuals, and deviation from back-calculated concentrations were also evaluated using in-house spreadsheets, package mvtnorm, 35,36 and the routines developed by B. Desharnais et al 30,31 LOD and LOQ were estimated by the Hubaux-Vos algorithm. Most validation parameters were determined from these data, including linearity range, limit of detection (LOD), LOQ, selectivity, specificity, trueness, accuracy, repeatability, and carry-over effect, in accordance with ISO/IEC 17025 and SWGTOX requirements.…”

“…The stepwise systematic method proposed by Desharnais et al 30,31 was used to select the most appropriate calibration model and validate and Grubbs tests). Lastly, no carry-over effect was observed.…”

“…The new analytical method was validated using a stepwise, analystindependent protocol that required the preparation of 7 independent calibration curves, 30,31 prepared in 3 different days, at 7 calibration levels: 2, 5, 10, 30, 50, 100, and 300 pg/mg. Most validation parameters were determined from these data, including linearity range, limit of detection (LOD), LOQ, selectivity, specificity, trueness, accuracy, repeatability, and carry-over effect, in accordance with ISO/IEC 17025 and SWGTOX requirements.…”

“…The linearity was checked by lack-of-fit and Mandel tests. 33,34 Determination coefficient (R 2 ), relative standard deviation of the slope, normality of the standardised residuals, and deviation from back-calculated concentrations were also evaluated using in-house spreadsheets, package mvtnorm, 35,36 and the routines developed by B. Desharnais et al 30,31 LOD and LOQ were estimated by the Hubaux-Vos algorithm. 37 Specificity was assessed by analysing 7 blank head samples from acknowledged teetotaller individuals; in particular, the presence/ absence of interfering ions on each single-ion chromatogram was evaluated, with reference to EtG pure standard.…”

“…All the results of significance tests are reported in the Supporting Information, together with the information about the slope and the intercept of the tested calibration model, and its determination coefficient, in the output format provided by the R codes developed and made available by Desharnais et al30,31 The whole procedure was repeatedly tested on a lower number of the already prepared calibration curves (ie, including 4 or 5 replicates only) to test the model robustness and similar results were obtained.From the final calibration model, LOD and LOQ values were calculated following the Hubaux-Vos' algorithm, 37 which yielded the following values: LOD = 0.8 pg/mg and LOQ = 1.7 pg/mg. The first step of the procedure involved the evaluation of data heteroscedasticity by means of F-test; then different statistical tests were executed, including lack-of-fit and normality testing, in order to choose the model order, either linear or quadratic, that best fitted the experimental calibration points (7 levels × 7 replicates), and the corresponding weighting.…”